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Approximation by functions with bounded derivative on Banach spaces

Published online by Cambridge University Press:  17 April 2009

R. Fry
R. Fry
Affiliation:
Department of Mathematics, St. Francis Xavier University, Antigonish, Nova Scotia, Canada, e-mail: rfry@stfx.ca
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Let X be a separable Banach space which admits a C1-smooth norm, and let G ⊂ X be an open subset. Then any real-valued, bounded and uniformly continuous map on G can be uniformly approximated on G by C1-smooth functions with bounded derivative.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 125 - 131
Copyright
Copyright © Australian Mathematical Society 2004

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